48 CATALOGUE Olf STARS WITHIN 
III. 
Inter-Adjustment of the Plates. 
The process next entered upon is the inter-adjustment of the results 
obtained from the different plates. Since the problem in question is 
similar to that discussed by Jacoby in the paper already referred to 
(Col. Con. no. 21), where the south polar plates are treated, the 
method devised by him will be followed here. A full statement of 
the problem is given on p. 7 of the above paper, and the method of 
solution on pp. 68-75. Its application in the present case is as fol- 
lows. The right ascensions and polar distances of the unknown stars 
upon any plate depend fundamentally upon the standard stars which 
appear upon that plate. For the 89° plates the number of standard 
stars on each plate varies from six to nine, and on the average four 
of these appear on two adjacent plates. Thus it may be expected, 
that, since the common data are so few, the agreement between the 
a's and t's of any particular star as found on two plates will not neces- 
sarily be very close. The largest actual residual from the mean in 
Table VI is i'''.03. Only ten residuals are greater than o". 75, and 
but twenty-five lie between o".6o and o".']^. 
The adjustment of these differences is carried out by means of 
equations (2), Publication i. These may be written in a more con- 
venient form without impairing the correctness of their derivation by 
assuming that the A' axis p jints to the vernal equinox, thus replacing 
the angle B by a. They then read : 
to sin ad'^ — CI) cos w^jj -|- pdA ' -\- (« — «') sin - = o , 
(2) 
— o) cos ad^ — w sin ad-^ -\- pdtv \- (tz — -') = o . 
These equations are general in their application. They express 
the relation of small changes in the constants t/l, drj, dA' and d^ to 
changes in the corresponding «'s and -'s without regard to the cause 
of the change. If the changes in the «'s and -'s of a sufficient number 
of stars arising from the same cause are known, the quantities d:, drj, 
dA' and do> may be obtained by the method of least squares. 
If on the other hand these corrections are known, the corrections 
Ja and J- to the positions of the stars may be computed. In the 
present case the quantities d^, etc., represent corrections to the plate 
constants of one plate which are required to adjust the «'s and -'s of 
the stars on that plate to a closer agreement with the «'s and -'s of 
